A square is drawn such that one of its sides coincides with the line \(y = 7\) , and so that the endpoints of this side lie on the parabola \(y = 2x^2 + 8x + 4\). What is the area of the square?
+128475 We just need to find the x intersection points of the parabola and the line y = 7
So....we have that
7 = 2x^2 + 8x + 4 subtract 7 from both sides
2x^2 + 8x - 3 = 0
Uing the quadratic formula
x = -8 ±√ [ 8^2 - 4(2)(-3) ] = -8 ±√ [ 88 ] = -8 ± 2√ 22 = -2 ±√22 /2 = - 4 ±√22
__________________ __________ _________ ________
2 * 2 4 4 2
So....the two points of intersection are - 4 + √22 and - 4 - √22
_______ _______
2 2
And the square of the distance between these points = the area of the square =
[ ( - 4 + √22) / 2 - ( -4 - √22) / 2 ] ^2 =
[ 2 √22 / 2 ] ^2 =
[ √22] ^2 =
22 units^2
